Anh T. Le and Timothy C. Steimle*

The molecular frame electric dipole

moment and hyperfine interaction in

hafnium fluoride, HfF. Department of Chemistry and Biochemistry, Arizona State

University,Tempe, AZ 85287

Petersburg Nuclear PhysicsInstitute, Gatchina, 188300, Russia

and Quantum Mechanics Division, St. Petersburg State University, St.

Petersburg 198904, Russia.

Leonid Skipnikov and Anatoly V. Titov

*Funded by NSF

The 68th International Symposium on Molecular Spectroscopy, June 2013

J. Chem. Phys. 138, 124313 (2013)

Electron’s Electric dipole moment measurement

PbO, YbF, PbF, ThO, WC, HfF+, HfH+, PtH+, PtF+, ThH+, ThF+...

small W-doubling easily polarized small Zeeman tuning.

Minimizes systematic errors

The 3D1 state:

Focus on HfF (not HfF+ ): Provide the hyperfine parameters, molecular dipole moments of

HfF

el HfF(theory) Calculated hyp. parameters, molecular dipole moments

Experimental values (hyp. Parameters, molecular dipole moments)

Comparisonel HfF+

Improve

PNC needed information (Wa, Ws, Wd)

Calculate

Previous Related Work on HfF – not much

Adam et al.(2004): J. Mol. Spectroc. 2004, 225, 1

Fine structure parameters for 9 bands in the range 17000-24000cm-1

Moskvitina et al.(1999):Spectrosc. Letts., 1999, 32(5), 719

Identify 3 bands: 589nm, 590.6 nm, 593.1 nm – Not analyzable

Motivated by eEDM experiments

Grau et al. (2012): J. Mol. Spectroc., 2012, 272, 32

8 bands recorded, rotationally assigned, analyzed 13400-14500cm-1

Barker et al. (2011):J. Chem. Phys. 2011, 134, 201102

REMPI study HfF, ZEKE study HfF+

Loh et al. (2012):J. Mol. Spectroc. 2012, 276-277, 49

REMPI study, transition in the excited state up to 33000cm-1

Experiment method

Ablation laser

CW dye laser

Skimmer

Stark Plates

Well collimatedmolecular beamRot.Temp.<20 K

Electric field > 4000 V/cmResolution ~30 MHz

Gated photon counter

%Abundance

I gN Q (mBarns

)177Hf 18.60 7/2 0.2571 +3365179Hf 13.62 9/2 -0.1574 +3793

180Hf 35.08 0 _ _

19F 100 1/2 5.376 _

Overview

177HfF R(11/2) 179HfF R(15/2)

NOTE: highly overlapped with 180HfF, Complicated spectra (WHY? Next slide)

Q (2H)=2.860(mBarns)

180HfF180HfF

Why are the spectra complicated ? (Cont.)177HfF R(11/2) (I=7/2)

J=5.5

X2D3/2

J=6.5

(v=1)[17.9]2.5

Rotation Mag. hyperfine(177Hf) [Mag.+Qua.] (177Hf)

9

8

7

6

5

4

3

2

10

9

8

7

6

5

4

3

F

9

8

65,7

4

3

2

10

83

9

7,6,5,4

F

J+I(7/2)=F

1. Effective Hamiltonian

Heff = Hso+ Hrot + Hmhf(Hf)+ HeQq(Hf)

Modeling the (1,0)[17.9]2.5-X2D3/2 band system

2. Matrix representation: Hund’s case (abJ) coupled basis set:

Eigenvalues & Eigenvectors

Parameters: B, h3/2(177,179Hf) and eQq0(177,179Hf) for the

X2D3/2(v=0) state,T00, B, h5/2(177,179Hf) and eQq0(177&179Hf) for the

[17.9]2.5(v=1) state

Observation & prediction 177HfF R(11/2)

Laser wavenumber (cm-1)

LIF

Sig

nal

Total Angular momentum, F

Rela

tive

Ener

gy L

evel

(cm

-1)

X2D3/2, J=5.5

(v=1)[17.9]2.5, J=6.5

ABCDEF

abcd

abcd

ABCDEF

ΔF=+1ΔF= 0

Observed

Pred.

180HfF

Observation & prediction of 179HfF R(15/2)(v=1)[17.9]2.5,

J=17/2

Rela

tive

Ener

gy L

evel

(cm

-1)

X2D3/2, J=15/2

LIF

Sig

nal

Laser wavenumber (cm-1)

A

B,C

G

DE

F H I K

ABCDEFGHIK

ΔF= +1

Observed

Pred.

180HfF

Stark Shift (MHz)

LIF

Sig

nal

(v=1)[17.9]2.5, J=5/2

X2D3/2, J=3/2

Electric Field Strength (V/cm)

En

erg

y S

hift

(MH

z)

1732.0 V/cm ||

1732.0 V/cm

Field FreeR(3/2)

Observation-Stark Shifts 180HfF

A B C D

a c e gb d f h

DCBA geca h fdb

ΔMF= 0ΔMF= -1

ΔMF= +1

Determined parameters

*CCSD(T) calculation - collaboration with Prof. Titov

gI(177Hf)

gI(179Hf)-1.59

hW(177Hf)

h W (179Hf)-1.68(16)

StatesX2D3/2

hW(179Hf)

[17.9]2.5 (v=1)

-0.00348(34) -0.01660(26)

0.02572(27)0.00586(38)hW(177Hf)

Predicted ratio

-1.55(3)

Q(177Hf)

Q(179Hf)0.89eQq0(177Hf)

eQq0(179Hf)

eQq0(177Hf)

eQq0(179Hf)

-0.0805(35) -0.2101 (43)

-0.1998(36)-0.0774(30)

0.96(8) 0.95(6)

0.0056(8)*

-0.0930(66) *

Para-meters

Discussion-Are the parameters realistic?1.Field Free Spectra

MO correlation diagram

h3/2(177HfF(experiment)): 176(11)MHz

Unpaired e is Hf-centered (5d2)

Predicted molecular magnetic

hyperfine parameter

h3/2(177Hf)=170 MHz

Atomic hyperfine of Hf

3F[Xe].4f14.5d2.6s2

…2s21d13s2 2D3/2

m(X2D3/2)=1.66(1) D

m([17.9]2.5(v=1))=0.419(7) D

Electron configuration of HfF

6s2(Hf)

mind mbond

mtot

Small m

F-Hf+

Why does HfF have small dipole moment?

2. Stark Spectra

Discussion-Are the parameters realistic?

(cont.)Determined molecular dipole moments:

Elec. Neg.Hf: 1.3F: 3.98

Large Dipole moment

Experiment:

Calculation CCSD(T): m(X2D3/2)= 1.63 D(collaboration with Prof. Titov)

Summary

• The molecular electric dipole moments of the

[17.9]2.5(v=1) and X2D3/2 (v=0) states from optical

Stark spectrum

• The complicated spectra of (1,0)[17.9]2.5-X2D3/2 have

been recorded and completely analyzed to provide

magnetic hyperfine and quadrupole parameters

• ab initio calculations using scalar-relativistic, coupled

cluster, method with single and double cluster

amplitudes (CCSD) of the 2Δ3/2 state properties were

performed by Prof. Titov. Calculated values are in

good agreement with the experimental values.

Thank you

NSF Funding sources:

Prof. Anatoly V. Titov (Petersburg Nuclear Physics

Institute)

Collaborations:

Group members: Dr. Fang Wang

Ruohan Zhang

Advisor: Prof. Timothy C. Steimle